Movement primitives via optimization

By Anca Dragan, Katharina Muelling, J. Bagnell, Siddhartha S. Srinivasa. 2015

65 citations recorded by the source corpus.

We formalize the problem of adapting a demonstrated trajectory to a new start and goal configuration as an optimization problem over a Hilbert space of trajectories: minimize the distance between the demonstration and the new trajectory subject to the new end point constraints. We show that the commonly used version of Dynamic Movement Primitives (DMPs) implement this minimization in the way they adapt demonstrations, for a particular choice of the Hilbert space norm. The generalization to arbitrary norms enables the robot to select a more appropriate norm for the task, as well as learn how to adapt the demonstration from the user. Our experiments show that this can significantly improve the robot's ability to accurately generalize the demonstration.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Learning from Physical Human Corrections, One Feature at a Time (2018, background): “Here ξ t is the robot’s current trajectory — optimal under θ t — and M is a matrix that smoothly propagates the local correction ∆qt along the rest of the trajectory [6].”
An Algorithmic Perspective on Imitation Learning (2018, methodology): “This formulation can be generalized to arbitrary norms, and Dragan et al. [2015] prove that trajectory adaptation with DMPs performs this norm minimization with a particular choice of the Hilbert norm, which is the same as the norm often used in trajectory optimization algorithms such as CHOMP Zucke”
Recent Advances in Robot Learning from Demonstration (2020, methodology): “For instance, demonstrations and reproductions can be viewed as minimizing a Hilbert norm, the parameters of which are to estimated (111).”
Learning Partially Contracting Dynamical Systems from Demonstrations (2017, methodology): “In [17], a geometric approach is proposed that adapts available demonstrations to new start and goal locations via optimization.”
Discovering Motor Programs by Recomposing Demonstrations (2020, background): “A few other works have approached the problem from an optimization perspective (Dragan et al., 2015).”
Towards Robust Skill Generalization: Unifying Learning from Demonstration and Motion Planning (2017, background): “[15] show that trajectory adaptation to new start/goal states via dynamic movement primitives (DMPs) [16] is a result of pre-specified Hilbert norm minimization based on finite differences, thus drawing connections to CHOMP [17], a gradient-based trajectory optimizer.”
Learning position and orientation dynamics from demonstrations via contraction analysis (2018, methodology): “Other categories of LfD methods include sampling-based methods (e.g., Bowen and Alterovitz 2014), optimization-based approaches (e.g., Dragan et al. 2015; Zucker et al. 2013), geometric methods (e.g., Ahmadzadeh et al. 2017), and key-frame-based methods (e.g., Akgun et al. 2012).”
Learning Robot Objectives from Physical Human Interaction (2017, methodology): “During experiments we here used a norm A based on acceleration [21], but we will explore learning the choice of this norm in future work.”